3.1: One-Step Equations
Learning Objectives
At the end of this lesson, students will be able to:
- Solve an equation using addition.
- Solve an equation using subtraction.
- Solve an equation using multiplication.
- Solve an equation using division.
Vocabulary
Terms introduced in this lesson:
- equal
- equation
- isolate
- linear equation
Teaching Strategies and Tips
Use the introductory problem to motivate equivalent equations, since it can be solved two ways:
- The cost plus the change received is equal to the amount paid, .
- The cost is equal to the difference between the amount paid and the change,
Examples 1 and 2 are essentially the same; constant terms must be added to both sides to isolate on the left. Adding vertically can benefit students.
Additional Example.
Solve .
Solution. To isolate , add to both sides of the equation. Add vertically.
The variable in Example 3 is not the usual . Remind students that the letter of the variable does not matter. Additional Example.
Solve .
Hint: To isolate , subtract from both sides of the equation.
In Examples 4-6, teachers may opt to solve the equations by adding the opposite in lieu of subtracting.
Example.
Solve .
Hint: To isolate , add to both sides of the equation. Add vertically.
Use Example 6 as an example of an equation with fractions. Remind students to find common denominators.
Point out in Example 8 that in general,
which will help students isolate in one step, multiplying by the reciprocal of .
Note that the equation in Example 10 can be written in dollars or in cents:
- ( in dollars)
- ( in cents)
Although Examples 13 and 15 can be solved by making a table and Example 14 by guessing and checking, teachers are encouraged to help students setup and solve an equation of the type presented in the lesson.
Error Troubleshooting
General Tip: After the constant term is canceled in a one-step equation, the variable must be carried down onto the next line. Remind students to write the .
General Tip: Students forget to perform the same operation on both sides of an equation. Have students use a colored pencil to write what they are doing to both sides of the equation.